Question

A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assuming a population standard deviation of 8.9 years, does this seem to indicate that the mean life span today is greater than 70 years

Answer 1

Answer:

We conclude that the mean life span today is greater than 70 years.

Step-by-step explanation:

We are given that a random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assuming a population standard deviation of 8.9 years.

Let Null Hypothesis, $\mu$ $\leq$ 70 years {means that the mean life span today is less than or equal to 70 years}

Alternate Hypothesis, $\mu$ > 70 years {means that the mean life span today is greater than 70 years}

The test statistics that will be used here is One-sample z test statistics;

         T.S. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean = 71.8 years

             $\sigma$ = population standard deviation = 8.9 years

             n = sample size = 100

So, test statistics = $\frac{71.8 - 70}{\frac{8.9}{\sqrt{100} } }$

                            = 2.022

Now, since we are not given with significance level so we assume it to be 5%. At 5% significance level, the z table gives critical value of 1.96. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it fall in the rejection region.

Therefore, we conclude that the mean life span today is greater than 70 years.

Answer 2

Answer:

This indicates that the chances of the mean life span today is greater than 70 years is 0.5871

Step-by-step explanation:

The past year showed an average life span of 71.8 years.

$\mu = 71.8 years$

Population standard deviation = 8.9 years

$\sigma = 8.9 years$

We are supposed to find the mean life span today is greater than 70 years

i.e. P(X>70)

Formula : $Z = \frac{x-\mu}{\sigma}$

$Z=\frac{70-71.8}{8.9}$

Z=−0.202

P(X<70)=0.4129

P(X>70)=1-P(X<70)=1-0.4129=0.5871

Hence This indicates that the chances of the mean life span today is greater than 70 years is 0.5871